A plate, 10 cm wide, 12 cm high and 1 cm thick, has a centrally located hole of 2 cm radius. The plate is subjected to a nominal (far-field) cyclic tensile stress of 100 MPa at R = 0. Two mode I fatigue cracks nucleate at the edges of the hole (as shown in Fig. 15.9) and propagate at a rate da/ dN = C(?K)3 , where C has a magnitude of 10-11 when da/dN is in units of m/cycle and AK is expressed in units of MPa.
(a) What is the transition crack size, lt, below which the growth of the fatigue crack is affected by the elastic strain field of the notch?
Assume small-scale yielding conditions at the tip of the fatigue crack and neglect the possibility of plastic deformation in the vicinity of the hole.
(b) If the crack initiates during the first stress cycle, calculate the number of fatigue cycles necessary to propagate the crack a distance of 1.5 cm on either side of the circular hole.
